Re: st: -manova- question

Jack Buckley <bucklesj@bc.edu> asks:
> I have a quick question about how -manova- calculates the Roy's
> largest root statistic. I am not a big MANOVA user, but I need to
> teach it in a multivariate course, so I have been working through
> some problems by hand from Rencher's excellent text, _Meth ods of
> Multivariate Analysis_. I found in the Statalist archive that if
> I run -manovatest- after estimation, the eigenvalues of the
> matrix [E^-1]H are saved in r(eigvals). Rencher states that Roy's
> largest root, theta, is computed simply by:
>
> theta = largest eigenvalue of [E^-1]H / (1+largest eigenvalue)
>
> when I work through problems and check the answers numerically in
> Stata, I find that everything is as expected except that Stata
> appears to report theta = largest eigenvalue of [E^-1]H
>
> Is this an alternative variant of Roy's statistic (i.e. is
> Rencher only describing one method in use) or is Stata computing
> a different quantity for some other reason, or (option three) am
> I just missing something obvious?
I too enjoy Rencher's books. I took my multivariate statistics
class from Rencher before the books existed -- his class notes
were the basis for his books.
Page 373 of "[R] manova" says (substitute greek symbols for
lambda and theta below):
"... Some authors report lambda_1, and others (including
Rencher) report theta = lambda_1/(1 + lambda_1) for Roy's
largest root. Stata reports lambda_1."
I hope you enjoy teaching the course.
Ken Higbee khigbee@stata.com
StataCorp 1-800-STATAPC
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